Erdfernerkundung - Numerische Physik: Modellierung

5.5. CAWSES 263
Abbildung 5.31: Specific energy
loss according to the Bethe–
Bloch equation for protons
[189]
In a dynamic magnetosphere, the same approach can be used, although it is pretty time
consuming.
The result of this model is a spatial pattern of precipitating particles on top of the atmosphere.
• a model to describe the ionization of the atmosphere by precipitating charged particles.
This will be described in detail below.
The result of such a model is an ion–pair production rate in the atmosphere, depending
on the horizontal coordinate (as inferred from the model magnetosphere above) and the
vertical coordinate (depending on the energy spectrum of the precipitating particles).
• a model to describe the chemistry of the atmosphere. Such a model includes a large number
of chemical reactions as well as some prescribed (or even self-consistently solved) transport
and needs the ion–pair production rates as input.
The result is a 2D or 3D (depending on the dimensionality of the model atmosphere) ozone
concentration that can be compared to the observations.
Thus the chain from observation 1 (SEPs in space) to observation 2 (ozone) leads through 3
models.
§ 870 For the present day magnetosphere, the horizontal pattern of precipitation and therefore
also ion–pair production is simple: SEPs precipitate inside the polar cap but not outside.
§ 871 The vertical pattern of ion–pair production is regulated by the spectrum of the incident
particles. The primary energy loss mechanism for charged protons in the energy range under
study is ionization. Formally, this process is described by the Bethe–Bloch equation
dE
dx
Z2 � 2 2mev
ne ln
v2 〈EB〉 − ln(1 − β2 ) − β 2
�
. (5.3)
= − e4
4πε 2 0 me
The specific energy loss dE/dx is the energy dE deposited per unit path length dx along
the particle track. It depends on (1) a number of constants (first fraction; the elementary
charge e, the electron mass me and the absolute permeability ε0), (2) the parameters of the
incident particle (second fraction: charge Z and speed v), and (3) the electron density ne of
the absorber. The first term in the bracket contain the relative kinetic energy compared to
the average bond energy 〈EB〉 in the target material. The remaining terms are relativistic
corrections with β = v/c.
§ 872 Figure 5.31 shows the specific energy loss depending on the particle energy for protons.
The specific energy loss decreases with increasing particle energy (interval 3) because the
c○ M.-B. Kallenrode 2. Juli 2008